COMBINATION OF MAPLE AND PYTHON CAPABILITIES TO CREATE A HYBRID ALGORITHM FOR NUMERICAL INTEGRATION OF COMPLEX FUNCTIONS

Abstract

The article explores the possibilities of computer mathematics (CMA) systems, in particular Maple and Python, for performing numerical integration of complex functions. Maple offers a number of unique capabilities, such as finding exact analytical solutions for many integrals, simplifying complex integrals before applying numerical methods, and identifying and handling features of the integral function. Maple's built-in system automatically selects the most appropriate integration method depending on the nature of the function. Maple also provides powerful visualization tools that can be used to graphically represent an integral function. Python, due to its flexibility and large number of libraries, is also a powerful tool for numerical integration. The NumPy, SciPy, and SymPy libraries provide efficient array manipulation, a wide range of algorithms for numerical analysis, and symbolic computation, respectively. Python allows you to easily create your own functions and classes for the implementation of specialized integration methods, including the implementation of new algorithms, the adaptation of existing methods for specific tasks, and the creation of complex computational models. The article proposes a hybrid algorithm that combines symbolic analysis in Maple with numerical integration in Python for efficient computation of complex integrals. The overall structure of the algorithm includes: analysis and preparation in Maple, data transfer from Maple to Python, numerical integration in Python, and analysis of the results with error estimation. An example of calculating a complex integral is considered, demonstrating the effectiveness of the proposed approach. Thus, the hybrid approach combining the symbolic capabilities of Maple with the numerical capabilities of Python allows for the creation of a reliable and efficient algorithm for the numerical integration of complex functions, ensuring high accuracy and optimization of the calculation process.